The strongly-constrained physics-informed neural network (SCPINN) is proposed by adding
the information of compound derivative embedded into the soft-constraint of physics …

Modulation instability (MI) is a pervasive phenomenon in nonlinear science. It is inevitable
for simulating rogue wave or breather solutions of the focusing nonlinear Schrödinger …

In this paper, we propose two new exponential integrator Fourier pseudo-spectral schemes
for nonlinear Dirac (NLD) equation. The proposed schemes are time symmetric …

This paper is concerned with a linearized second-order finite difference scheme for solving
the nonlinear time-fractional Schrödinger equation in d (d= 1, 2, 3) dimensions. Under a …

In this paper, two novel conservative relaxation methods are developed for the space-
fractional nonlinear Schrödinger equation. The first type of relaxation scheme adopts the …

In this letter, we present two novel classes of linear high-order mass-preserving schemes for
the generalized nonlinear Schrödinger equation. The original model is first equivalently …

Fast high-order compact finite difference schemes are investigated for solving the two-
dimensional nonlinear Schrödinger equation with periodic boundary conditions. These …

Two conservative and linearly-implicit difference schemes are presented for solving the
nonlinear fourth-order wave equation with the periodic boundary condition. These schemes …

In this paper, an adaptive gradient-enhanced physics-informed neural network method (A-
gPINN) is proposed to investigate the dynamics of solitons in tapered refractive index …

The Fourier pseudo-spectral method is well suited to solve PDEs under the periodic
boundary condition due to its high-order accuracy and easy-to-implement feature. In this …